A Theory of Electrons and Protons

The relativity quantum theory of an electron moving in a given electro­magnetic field, although successful in predicting the spin properties of the electron, yet involves one serious difficulty which shows that some fundamental alteration is necessary before we can regard it as an accurate description of nature. This difficulty is connected with the fact that the wave equation, which is of the form [W/ c + e / c A + ρ1 (σ, p + e / c A) + ρ3 mc ] Ψ = 0, (1) has, in addition to the wanted solutions for which the kinetic energy of the electron is positive, an equal number of unwanted solutions with negative kinetic energy for the electron, which appear to have no physical meaning. Thus if we take the case of a steady electromagnetic field, equation (1) will admit of periodic solutions of the form Ψ = u e - i E t / h , (2) where u is independent of t , representing stationary states, E being the total energy of the state, including the relativity term mc 2. There will then exist solutions (2) with negative values for E as well as those with positive values ; in fact, if we take a matrix representation of the operators ρ1σ1, ρ1σ2, ρ1σ3, ρ3 with the matrix elements all real, then the conjugate complex of any solution of (1) will be a solution of the wave equation obtained from (1) by reversal of the sign of the potentials A, and either the original wave function or its con­jugate complex must refer to a negative E.